With large tobacco companies attempting to tap into the fast-growing market for electronic cigarettes, analysts at Bank of America Merrill Lynch believe that British American Tobacco (BAT) could benefit from the buy-out of one of its smaller rivals.According to a research report from the bank on Monday, it would be "advantageous" for BAT to acquire the 58% of US smaller peer Reynolds American (RAI) that it does not already own.There has been renewed speculation in the market that BAT could buy RAI following reports about a possible merger between RAI and US peer Lorillard (LO) earlier this month.BofA said that a RAI buy-out would "make sense both financially and strategically" for BAT."If a RAI-LO combination is possible, we think that, from BAT's point of view, it would make much more sense for BAT to buy RAI, and then at some point buy LO later, than allow RAI to combine with LO, and then try to buy the combined entity," the bank said.BofA speculated that a possible takeover of RAI would be made at $65-75 a share, compared with RAI's current price of around $54, and would be 10-13% earnings per share accretive to BAT. "Strategically it would give BAT total freedom to deploy RAI's intellectual property on e-cigs (Vuse) and heat-not-burn wherever it wanted to globally. This is important because US consumers have demonstrated a strong preference for Vuse."The bank said that this takeover option reinforces its positive view on BAT as it including the stock in its 'European Focus' list.BAT was trading more or less flat on Tuesday.BC